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Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…
Programs admitting a polyhedral representation can be transformed in many ways for locality and parallelism, notably loop tiling. Data flow analysis can then compute dependence relations between iterations and between tiles. When tiling is…
Correctness proofs for floating point programs are difficult to verify. To simplify the task, a similar, but less complex system, known as logarithmic arithmetic can be used. The Boyer-Moore Theorem Prover, NQTHM, mechanically verified the…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…
In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…
Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…
The Posit Number System was introduced in 2017 as a replacement for floating-point numbers. Since then, the community has explored its application in Neural Network related tasks and produced some unit designs which are still far from being…
In modern low-power embedded platforms, floating-point (FP) operations emerge as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
Recently, a novel method based on coding partitions [1]-[4] has been used to derive power series expansions to previously intractable problems. In this method the coefficients at $k$ are determined by summing the contributions made by each…
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…